A remark on divisibility of definable groups

We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and p_k : G → G is the definable map given by p_k (x ) = x^k for all x ∈ G , then we have |(p_k )^–1(x )| ≥ k^r for all x ∈ G , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Dienone–Phenol Rearrangement of Santonin: A Comprehensive Laboratory Experiment for Advanced Undergraduate Organic Chemistry Students

A comprehensive laboratory experiment suitable for advanced undergraduate organic chemistry students has been designed. The experiment is based on the dienone-phenol rearrangement reaction of the sesquiterpene santonin to give -desmotroposantonin acetate. It challenges students to solve an earlier controversial stereochemical problem. The students carry out the reaction and analyze spectroscopic data to determine the stereochemistry of the starting material and the product. In addition, they perform simple molecular modeling calculations, which enable them to rationalize the stereochemical outcome of the transformation and discuss the mechanism of the dienone-phenol rearrangement and related rearrangements reported in the literature.     

New analytic properties of nonstandard Sobolev-type Charlier orthogonal polynomials

Numerical Algorithms - In this contribution, we consider the sequence $\{Q_{n}^{\lambda }\}_{n\geq 0}$ of monic polynomials orthogonal with respect to the following inner product involving...     

Overexpression in Catharanthus roseus hairy roots of a truncated hamster 3-hydroxy-3-methylglutaryl-CoA reductase gene

Catharanthus roseus (L.) G. Don hairy roots harboring hamster 3-hydroxy-3-methylglutaryl-CoA reductase (HMGR) (EC 1.1.1.88) cDNA without membrane-binding domain were evaluated by quantifying the levels of sterols and some indol-alkaloids. Clone 236, with the highest hybridization signal, had the lowest soluble and microsomal HMGR activity and produced more ajmalicine and catharanthine than the control but had reduced campesterol concentration. Clone 19, with low hybridization signal, had high soluble HMGR activity and produced high levels of campesterol and five to seven times more serpentine than the control but a low level of ajmalicine and no accumulation of catharanthine. These results suggest a possible role for HMGR in indole alkaloid biosynthesis and a possible cosuppression of both the endogenous and foreign HMGR genes in clone 236.     

Diastered and Regiochemical Control in the Functionalization of the Allylic [dbnd] of a Natural 5-(1-Alkenyl)-2-Enono-1,5-Lactone

The diastereo and regioselectivity of the bromohydrination of argentilactona [(5R)-(-)-δ-lactone of 5-hydroxydodeca-Z, Z-2,6-dienoic acid] and the regioselectivity of the aqueous acidic opening of its 65,75 and 6R,7R-epoxides were studied. Although the reactions occurred with low diasterofacial control, the regioselectivity observed in all cases was high, suggesting that the sequences could be of some synthetic value.     

Stereoselective enzymatic synthesis of monoglucosyl-myo-inositols with in vivo anti-inflammatory activity

The monoglucosyl-inositols α-d-glucopyranosyl-(1→4)-4d-myo-inositol 3 and α-d-glucopyranosyl-(1→1)-1d-myo-inositol 4 were synthesized by a combined enzymatic transglucosylation and hydrolysis strategy, using cyclodextrin glucosyl transferase (CGTase) from Thermoanaerobacter sp., followed by hydrolysis with Aspergillus niger glucoamylase. The glucosides were separated by preparative HPLC and fully characterized by extensive 1D and 2D NMR studies. The structure of the regioisomer 4 was confirmed by X-ray crystallography of its perbenzoylated derivative 4a. Both isomers demonstrated in vivo anti-inflammatory activity at comparative levels to corticosterone on mouse ear oedema induced by 12-O-tetradecanoylphorbol-13-acetate (TPA) and in rat hind paw oedema induced by carrageenan.     

Invariance results for definable extensions of groups

We show that in an o-minimal expansion of an ordered group finite definable extensions of a definable group which is defined in a reduct are already defined in the reduct. A similar result is proved for finite topological extensions of definable groups defined in o-minimal expansions of the ordered set of real numbers.     

On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation

In this paper, by means of Banach fixed point theorem, we investigate the existence and Ulam–Hyers–Rassias stability of the noninstantaneous impulsive integrodifferential equation by means of ψ‐Hilfer fractional derivative. In this sense, some examples are presented, in order to consolidate the results obtained.     

Thermodynamics of the xenon + methyl chloride system

The total vapour pressure of the xenon + methyl chloride system has been measured as a function of composition at 175.44 and 182.32 K. The resulting data have been used to evaluate the excess Gibbs functions G^E at the same temperatures. The excess enthalpy and excess molar volume have also been measured at 182.32 K. The system shows large positive deviations from Raoult's law but negative volumes on mixing. These results are compared with theoretical predictions of a recent molecular theory and of standard engineering methods. The calculations show the superiority of the molecular theory over more empirical procedures such as those based on the Redlich-Kwong equation of state or the regular-solution model.     

Determination of natural uranium by various analytical techniques in soils of Zacatecas State (Mexico)

Journal of Radioanalytical and Nuclear Chemistry - 238U is a radionuclide present in the earth’s crust that provides 65.9% of annual average radiation dose and represents 99.27% of total...